To analyze the system of equations given for savings accounts at Acorn Bank and Dewberry Savings and Loan, let's break down the constraints:
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Time Constraint (x): Normally, the number of years (x) cannot be negative, hence:
- The constraint on time is \( x \geq 0 \).
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Balance Constraint (y): The balance (y) after any number of years (given the initial amounts and compounded interest) will also start from a positive value:
- Both accounts start with a positive initial balance, so it stands to reason that the balance will also be greater than or equal to 0.
For Acorn Bank, the balance will start at $1500 and grow from there. For Dewberry, it will start at $1200 and also grow. Therefore, y will be greater than or equal to both of the initial amounts, but still greater than or equal to 0 overall.
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First Quadrant Viability: Since both x and y must be non-negative for a financial context (years cannot be negative and the balance cannot be negative), the solutions are restricted to the first quadrant of the coordinate plane.
With all this said, the correct interpretation based on the constraints would be:
- The constraint on time is \( x \geq 0 \).
- The constraint on the balance is \( y \geq 0 \).
- The viable solution will indeed be in the first quadrant.
Thus, the correct choice from your responses is:
The constraint on time is \( x \geq 0 \). The constraint on the balance is \( y \geq 0 \). The viable solution will be in the first quadrant.
2 answers